One of the demonstrations for the existence of God is the Kalam Cosmological Argument, which claims that the universe had a beginning, and therefore needed a beginner. At its root, it is quite simple, for anything that comes to be must have a cause. Of itself, the Kalam demonstration does not get us the God of the Bible, but further reasoning after the Kalam can get us to God’s attributes.

One of the supports for the demonstration is that there cannot be an infinite series of moments prior to now, so there must be a beginning. Most of the arguments about infinites in Kalam are dealt with by those philosophically trained theists who understand the Kalam. Perhaps the leading supporter of Kalam is William Lane Craig, whose book The Kalam Cosmological Argument has a lengthy section on infinity. Craig also includes 25 pages of detailed defense of his position on infinity in The Blackwell Companion to Natural Theology.

Skeptics and atheists are not silent on this point, of course, and have fun entangling theists in conundrums about infinites. I’m convinced most of them do not read the detailed explanations in the writings of men like Craig, but either get their information from popular online sources such as YouTube or do not listen to theists at all, but merely pass around criticisms among themselves. If they would have read the detailed explanations of Kalam, they would not make the same mistakes over and over.

One of the key positions of the Kalam argument is that the there cannot be an infinite series of moments prior to now, so there must be a beginning. One of the supports for this is the following:

A collection formed by successive addition cannot be an actual infinite.

The temporal series of events is a collection formed by successive addition.

Therefore, the temporal series of events cannot be an actual infinite. (Craig, Natural Theology, p.117)

Skeptics respond with a series of criticisms, most of which are off point. They give arguments such as infinity being used in mathematics. Indeed, interesting and odd things can be found when one tries to nail down the properties of infinity. For example, the mathematician Bolzano (1781 – 1848) pointed out that if we take the simple function y=2x, and apply it to all the numbers between 0 and 1, then “every real number between o and 1 is assigned a unique companion between 0 and 2. Therefore, Bolzano concluded, there are as many numbers between 0 and 1 as there are in the interval 0 to 2, which has twice the length of the 0 to 1 interval.” (Aczel, The Mystery of the Aleph, p.61).

Further, we can take an infinite set of whole numbers, and compare it to an infinite set of odd numbers, and an infinite set of squared numbers, and the different sets will be the same size: infinite. Such are the games people play with defining infinity.

The problem, of course, is that these are mathematical abstracts, not actual infinity. Craig’s point in Kalam is not denying that we can do slippery things in mathematics with infinity – no one in apologetics denies that. The Kalam denies actual infinity that is reached by successive addition. This is a very different thing than abstract infinity in math formulas, or possible numbers between two points. We can indeed do math that shows an infinite set of numbers within an inch. However, no matter how hard we try, we cannot add an infinite number of sheets of paper into a one-inch binder. No matter how thin the paper, or how hard we squeeze, we can only add a finite number of sheets of paper into one inch.

The Kalam also deals with successive addition. It is a brute fact that in a series derived by successive addition, we always have an ever-increasing finite, not an infinite. As Craig explains:

It follows, then, that the temporal series of events cannot be actually infinite. The only way a collection of which members are being successively added could be actually infinite would be for it to have an infinite tenselessly existing “core” to which additions are being made. But then, it would not be a collection formed by successive addition, for there would always exist a surd infinite, itself not formed successively but simply given, to which a finite number of successive additions have been made. (Natural Theology, 124-125)

As apologists, we find ourselves repeatedly having to explain that in dealing with objects in the universe being measured by moments of time, we are dealing with actual, real things, not abstract distances between two points on an imaginary timeline. We are dealing with actual, real things that are occurring successively. Adding to very large finites merely gives us bigger finites.

There is a group that is trying to build a clock that will run for 10,000 years. Let’s say they succeed. We can be sure of two things. First, it may run for a long time, but it will not run forever, for eventually the forces of nature will stop it. Second, if someone finds it someday, they will be able to conclude that since it is running, someone had to start it. It could not have been running for an infinite amount of time.

In the work of Craig and other theists who specialize in the Kalam, they deal with much more detail than can be done on this blog. I still wonder if the skeptics have truly read the detailed explanations of Kalam. I also wonder if they truly believe their positions, or if they just like to have fun slipping around in the world of abstract infinity. In the end, the Kalam Argument is a valid demonstration that shows the universe had a beginning and therefore needed a Beginner.

So, if there can not be an infinite series of moments, so what. Do you think that time exists outside of this universe and that there is no possible way that anything could have existed prior to the big bang? If so, why? What reason would you have for thinking that?

Please define both ‘exist’ and ‘begins to exist’ so that the conversation is understood on both sides.

The “so what” is that logically, there must have been a beginning of moments, and things with beginnings require a cause. Therefore logically there must be a timeless cause for the universe. Atheists are so aware of the consequences of this that they do gymnastics trying to avoid the consequences of a beginning.

Time is change in relation between things, and can exist anywhere there is change. “15 minutes” is only meaningful in the sense of a certain degree of change between the earth and the sun.

As to speculating ideas about changing existence prior to the big bang, we have no evidence of such a thing, and I prefer to deal with what we can know logically based on evidence. It is generally not fruitful to engage in pure “it may have been” ideas when we have no evidence to base it on. I prefer to deal in the world of evidence, logic, and reason. Hawking, for example, has proposed an idea of the universe existing in a dimension prior to this one, where the big bang was merely the universe moving between dimensions. Such ideas are pure speculation based on no evidence, and do not avoid the problem presented in this post — it merely pushes the inevitable back further in time. It’s turtles all the way down.

As to the definition of existence, this is a question for metaphysics. I would follow a standard Thomist / Aristotelean definition, namely, “an act of being insomuch as it is.” But that won’t mean much unless you’ve studied metaphysics, which is a different topic for a different post. If I recall correctly, I’ve dealt with Hawking’s mistakes and being in other blog posts.

I believe that your definition of time is skewed and tainted by your existence within the framework of space-time in which we find ourselves. In non-3d space relationships are not as you find them in this universe. Einstein has shown that time and space are intertwined such that outside of the space of this universe time would be different if it exists or is experienced. If ‘begins to exist’ has a time component then a thing can only begin to exist within the framework inside of this universe that we know.

If you wish to presuppose that time is experienced similarly outside and inside this universe then it is fair to say that outside this universe is not absolutely nothing. At this point the definition of ‘begins to exist’ becomes fairly important. Does a rain drop ‘begin to exist’? To claim that the universe we know ‘began to exist’ requires evidence that nothing existed prior to it. A claim that you can not in good faith make.

An infinity of moments is just as likely to be an absurd notion outside of our space time as it is to be impossible, just as an invisible mountain is an absurd notion inside our space time.

If you believe that a rain drop begins to exist, what is the cause? How far back do you go with the cause/effect chain to say what is the beginning of the rain drop? Please explain why the stop on infinite regress has to happen just prior to the big bang? It seems a rather simplistic and confoundingly arbitrary place to put a stop and say god did it. Why can’t your creator god have created 43 other levels of existence concentrically surrounding this one? Do you know the mind of your god?

Finally, why is something outside of our space time such that it can only be _your_ god? Maybe there are gods and there are millions of them, or infinite numbers but you only know the one? Maybe there are no gods at all and this universe is much like a rain drop in the larger picture?

As I said in the post, based on your questions and objections, I do not believe you have read the detailed explanations of Kalam, for they are answered in the literature, and some are answered in this post. To summarize: First, as the post says, the whole point of the Kalam argument is that there is not an infinite series of moments, inside or outside of the universe. There must have been a beginning of them, whether in our out of the universe. (Which, btw, in a purely materialistic universe, “outside the universe” is either an equivocation or an impossibility.) We would agree that an infinite series is absurd….that’s the whole point of the argument. Second, as the post says, the Kalam does not get us to the God of the Bible, but logical application after Kalam gets us to God’s attributes. Again, read the literature. Third, a raindrop, in the sense of metaphysical beginning, is not a beginning but a becomming. The water exists prior to the raindrop, it merely becomes a raindrop. No existence is added, merely accidents. (again, metaphysics). Such is not the case in the big bang, for the evidence does not point to a becomming, but to a beginning. Argument to the contrary is speculation not based in evidence. Fourth, you said “To claim that the universe we know ‘began to exist’ requires evidence that nothing existed prior to it.” Logically, the answer is just the opposite; As the Kalam states, anything that begins to exist must have a cause. The point of all cosmological arguments is that anything that begins to exist must have a cause. If we deny this, we deny the basis for all knowledge, science, and logic, and go the realm of things coming to exist from nothing with no cause, a clear absurdity that we deny. Again, I prefer to stay in the area of evidence, logic, and reason. Fifth, while I admit I am not a theoretical physicist, as I understand Einstein, his theories are perfectly compatible with time being a measure of the change in relation between two things. All known evidence points to this, any argument to the contrary is not based on empirical evidence.

I may not have been clear……your point on “begin to exist” requiring a prior time and cause is partially valid. While a beginning of existence does require a prior cause, the universe itself is being. Prior to being is non-being, and non-being has no attributes. In the Kalam, the prior cause is changeless, and unique, therefore time is meaningless. There is a logically prior cause, but since time began with the creation of matter, there is nothing that is chronologically prior. Time before time is absurd, as you have noted. Actually, we observe nothing begin to exist within the universe, but only change and becomming. Supporters of Kalam deal with all these questions in the technical literature, which I would encourage you to read.

Well put. Infinites routinely utilized by cosmologists are of the type that can be manipulated quite readily. Even so, there remains the (in principle, and I think) insurmountable reification problem to deal with. Max Tegmark et al have postulated infinite universes, in numerous spatial dimensions, that may or may not coalesce with the dimension in which we find ourselves. Though interesting to ponder, these types of hypothetical realms—even if they could exist—have very little to say regarding the one spatial dimension we are cognizant of. These other dimensions are necessarily undetectable. Moreover, each is yet subject to its own infinite regress. More modest proposals, such as those posited by Alan Guth and others, undoubtedly face similar objections with respect to their own necessarily finite beginning.

What I find interesting is the fact that many lay persons take these cosmological speculations at face value, as if they somehow overcome the multifaceted problems facing infinites. A basic distinction—as you noted—should be made here concerning indefinites (potential infinites) and actual infinites. The latter cannot be instantiated, on my view. Of course, an ever expanding universe has the potential to continue indefinitely; nevertheless, from any moment in the future, a hypothetical observer—whether angel or God himself—will be able to look back at a finite number of days or years since its inception.

Another tack is to hypothesize, a la Stephen Hawking, that the positive energy in the universe is equal to the negative energy; therefore, the universe simply exists (as a brute fact), even though it has a space/time boundary in the finite past. But, this view also fails to take into account that numbers—and hence all equations—are causally effete. Equations and formulas are merely descriptors of phenomena, and not the phenomena themselves. At the end of the day, all that remains to support this view is a host of mathematical calculations; not a perpetual universe actualized by nothing—or rather, by equilibrium.

The post very briefly mentions that any series created by successive addition is an ever-increasing finite, which is always a finite, not an infinite. As the quote by Craig summarizes, the only way successive addition can be construed to be an infinite is if some sort of collection is assumed from the start, which would not be created by successive addition. It is a brute fact that adding together large finites result in more finites.

But as this post states, it is but a brief summary, mainly pointing out that the Kalam argument is built upon an actual collection created by successive addition, not upon some abstract concept of mathematics.

For a more thorough explanation, see the two books referenced in the post, The Kalam Cosmological Argument and The Blackwell Companion to Natural Theology.

Let us assume a timeline without a begin or end. Now place anywhere on the line two points. Measure the distance. The fact is, no matter where you placed those points, the distance is strictly finite. This is now the real infinite, which exists solely in the form of finites! The infinite is full of such contradictions, and any way to solve them leads to worse contradictions.
The concept of an infinite as something already absorbed is of course something complete contradictionary, because the infinite can not be completely absorbed.

It is just because infinity is a contradiction that it is an infinite process, unrolling endlessly in time and in space.

The presumed paradox that time can not be past eternal, because it would form an “actual infinity” is false, since in reality, only the ever ongoing moment in time of “now” exists – the past moments no longer exists, the future moments do not yet exist.

If it were the case that all moments of time were to exist “simultaneously”, then yes, that would be a contradiction. But that is appearently NOT what time is!

So, give up the wrong idea that moments of the past or the future exist, and you’ll be fine!

Even though the presumed contradiction of an “actual infinity” of time, assumed on time without a begin or end, is invalid (see the argument above) – so time may well be infinite and without begin or end – the conclusion is still a conclusion which holds only in abstact reality. In physical reality, we need to confirm such things, based on real physics. Things might be different there.

One of such limitations is that in a classical spacetime that on average is expanding, the spactime is not past-complete (Borde-Guth-Vilenkin). Cosmologies that have an eternal past, are not necessarily impossible, there are ways the theorema can be circumvented. For example if the past-complete spacetime were non-classical (quantum mechanical).

But that would bring in the issue that the measurability of spacetime would become impossible. Without matter in the form of masses (classiclly described), no rulers or clocks exist. That is not to say that no space or time exist, but it can’t be measured.

Without a unified theory about gravity and quantum field theory, we can at the moment not say something definite about it. Cosmology sees it as an open question.

So a finite is an infinite. That’s news to me, and I must admit, a novel approach. For me, I’ll stick with finites and infinites being different things, since that is the first law of logic.

Whether or not the past currently exists will not impact the conclusions in the post. We can still measure change. If we could not, then we would not have much to discuss, since the entire conversation hinges upon measuring change.

Therefore, as the post states, an addition of finites still is a finite at all points.

Time is merely a measure of change in relation. “Fifteen minutes” is only relevant in terms of a change in earth rotation in relation to the sun. Without that change, “fifteen minutes” means nothing. Therefore time is not a metaphysical state of being, but merely a measure of change. Past and present are only meaningful in relation to change. That is shown in other posts on this blog. This post still stands.